N Queens (recursive backtracking thought)

Eight queens problem is an old and well-known problem is backtracking algorithms typical cases. The problem is an international chess player Max Bethel presented in 1848: placed on the international chess 8 × 8 grid of eight Queens, it can not attack each other, that any two queens can not be in the same line, on the same row or the same slash and asked how many pendulum method.

Thus come to develop N Queens

The number of first seeking the solution: // backtracking algorithm is the brute-force method

1. Each row put a queen

2. Lower the line when the judge: Will there be the same column, will appear the same slash. The slope determination can be attributed to slash Analyzing.

// recursive backtracking code is as follows: 
#include <the iostream>
 the using  namespace STD; 
#include <math.h>
 #define N 16
 int n-; // number Queen 
int SUM = 0 ; // number of feasible solutions 
int X [N ]; // tag Queen columns placed 

BOOL the Agree ( int K) 
{ 
    int I;
     for (I = . 1 ; I <K; I ++ )
         IF (ABS (K - I) == ABS (X [K] - X [I]) || X [K] == X [I])
             return  to false ;
     return  to true ;
} 

Int Queen ( int T) 
{ 
    IF (T> n && n> 0 ) // when placed Queen exceeds n, the number of feasible solutions plus 1, where n must be greater than 0 
        SUM ++ ;
     the else 
        for ( int I = 1 ; I <= n-; I ++ ) 
        { 
            X [T] = I; // tag 
            IF (the Agree (T)) 
                Queen (T + . 1 ); 
        } 
    return SUM; 
} 

int main () 
{ 
    int T; 
    CIN >> n-; 
    T = Queen (1);
    cout << t;
    return 0;
}

Since then supplemented iteration ---------------- ------------------ backtracking algorithm